Prep the pan and oven. Heat oven to 350°F (175°C). Line a square pan with parchment, leaving overhang for easy lifting. Lightly grease the paper.

Make the brownie batter. Melt butter in a saucepan or microwave-safe bowl. Whisk in granulated and brown sugars until glossy. Let cool 2 minutes, then whisk in eggs and vanilla until smooth.

Add dry ingredients. Sift in flour, cocoa powder, and salt. Add espresso powder if using. Stir just until no dry spots remain. Fold in chocolate chips if you like. Batter will be thick and shiny.

Spread the base. Scrape about 90% of the brownie batter into the pan. Smooth it into an even layer. Reserve the rest for topping dollops.

Beat the cheesecake layer. In a bowl, beat softened cream cheese until smooth, 30–45 seconds. Add sugar and a pinch of salt and beat until creamy. Mix in sour cream, egg, and vanilla until just combined and silky.

Add the matcha. Sift matcha powder over the cheesecake mixture to avoid lumps. Whisk or beat on low until evenly green. Taste and adjust: add a little more matcha for a stronger, earthier note.

Layer and swirl. Pour the matcha cheesecake over the brownie base and smooth the top. Dot the remaining brownie batter over the cheesecake in small spoonfuls. Drag a butter knife or skewer through the dollops in gentle figure-eights to create swirls. Don’t over-swirl or colors will blend.

Bake. Place on the middle rack and bake 30–38 minutes, depending on pan size and oven. The edges should be set and the center slightly wobbly but not wet. A toothpick inserted near the edge should come out with a few moist crumbs.

Cool and chill. Let the pan cool on a rack until room temperature. Then cover and chill at least 2 hours (overnight is best) for clean slices and the creamiest texture.

Slice and serve. Lift out using the parchment. Use a warm, dry knife for neat edges, wiping between cuts. Serve as is or with a light dusting of matcha or a few raspberries on the side.